Resumen de Using CAS to Show Chaos Game Representations Of DNA Sequences
In 1990, H. J. Jeffrey wrote a paper describing what he called the Chaos Game Representation of gene structures. The Chaos Game is essentially an Iterated Function Scheme, similar to that used in the representation of the Sierpinski Triangle obtained by plotting a sequence of points generated in a somewhat random fashion. Jeffrey replaced the triangle with a square and the random selection process with the use of a DNA sequence read from its left end to the right end. Observing the patterns that these sequences generated Jeffrey was able to make some fundamental observations about the genomic structure and origins of the sequence. He also noticed certain phenomena about the nature of the pattern generation.
Jeffrey's paper also led to more advanced work on Chaos Game Representations by researchers in molecular biology, particularly the research groups lead by Almeida in 2001, and that of Deschavannein 1999, and followed by the work of Joseph and Sasikumar in 2006.
In this paper we will develop the Chaos Game Representation and Jeffrey's conclusions. We will show how using the rational arithmetic found in Computer Algebra Systems enhances the accuracy of plotting the representations. Finally, we note the contributions of the later research to the alignment of either 2 or more DNA sequences.
